On a didactic remark

N. Lygeros

« It is almost a miracle that modern teaching methods have not yet entirely strangled the holy curiosity of inquiry; for what this delicate little plant needs more than anything, besides stimulation, is freedom. » Albert Einstein

In fact we can generalize the previous didactic remark to all procedures of ignition in brainstorming. Especially with the resolution of open problems, the freedom factor is one of the most important heuristic tools. As non-uniform reasoning has to start with a different approach, it is often impossible to simply apply a classical methodology. Therefore the use of freedom is almost a necessity in this cognitive field. The nature of freedom is so hard to define that we prefer to use the notion of obstruction to characterize it in an indirect way. And this difficulty proves the importance and the wide spectrum of freedom in research. Unfortunately it is very hard to teach students how to use their freedom to solve specific open problems, so professors usually tend to explain methods even if they know that they can not be generalized to those specific problems. They prefer to consider classical and typical problems rather than others to avoid the existence of singularities in the resolution. In other words, they only consider problems without methodological or heuristic problems. Therefore the students naturally think that this category of problems represents the reality of problems which is obviously false. That's why they prefer to have guidelines rather than freedom when they have to solve a problem. Consequently it is very rare for them to witness the power of freedom and its effectiveness in real problems which are not academic or toy problems. In fact, especially for gifted students, freedom has to be explained on the basis of several open problems which can be considered as paradigms of complexity in resolution theory to increase their potential but also to use their potential. Only freedom enables to transcend didactic difficulties.

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